Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society

, Volume 20, Issue 1, pp 113–133

Expansive homeomorphisms of surfaces


  • Jorge Lewowicz
    • Instituto de Matemática y Estadística Prof. Ing. Rafael Laguardia

DOI: 10.1007/BF02585472

Cite this article as:
Lewowicz, J. Bol. Soc. Bras. Mat (1989) 20: 113. doi:10.1007/BF02585472


Letf be an expansive homeomorphism of a compact oriented surfaceM. We show thatS2 does not support such anf, and thatf is conjugate to an Anosov diffeomorphism ifM=T2, and to a pseudo-Anosov map ifM has genus ≥2. These results are consequences of our description of local stable (unstable) sets: everyxM has a local stable (unstable) set that consists of the union ofr arcs that meet only atx. For eachxMr=2, except for a finite number of points, wherer≥3.

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© Sociedade Brasileira de Matemática 1989